Three rods are arranged in the form of an equilateral triangle. Calculate the moment of inertia about an axis passing through the centroid and perpendicular to the plane of the triangle. (Each rod has mass $M$ and length $L$)

$M$ and $R$ are the mass and radius of a disc. $A$ small disc of radius $R/3$ is removed from the bigger disc as shown in the figure. The moment of inertia of the remaining part of the bigger disc about an axis $\text{AB}$ passing through the centre $O$ and perpendicular to the plane of the disc is $\frac{4}{x} MR^2$. The value of $x$ is . . . . . . .

Consider a thin uniform square sheet made of a rigid material. If its side is $a$,mass is $m$,and the moment of inertia about one of its diagonals is $I$,then:

According to the parallel axis theorem,$I = I_C + Mx^2$. Which of the following graphs of $I$ versus $x$ is correct?

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed concentrically. If the mass of the removed disc is $M$,what is the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre?

From a disc of radius $R$,a concentric circular portion of radius $r$ is cut out so as to leave an annular disc of mass $M$. The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is